Related papers: Path components of $\mathrm{G}_2$-moduli spaces ma…

Building on previous works by Bilu, Chambert-Loir and Loeser, we study the asymptotic behaviour of the moduli space of sections of a given family over a smooth projective curve, assuming that the generic fiber is an equivariant…

The moduli space of canonical divisors (with prescribed zeros and poles) on nonsingular curves is not compact since the curve may degenerate. We define a proper moduli space of twisted canonical divisors in the moduli space of…

Let G be a finite group of exponent m and let k be a field of characteristic prime to m, containing the m-th roots of unity. For any Rost cycle module M over k, we construct exact sequences detecting the unramified elements in Serre's group…

We give a new construction of noncommutative surfaces via elliptic difference operators, attaching a 1-parameter noncommutative deformation to any projective rational surface with smooth anticanonical curve. The construction agrees with one…

It is known that there exist complex solvmanifolds $(\Gamma\backslash G,J)$ whose canonical bundle is trivialized by a holomorphic section which is not invariant under the action of $G$. The main goal of this article is to classify the…

Let $X\rightarrow Y$ be a Galois cover with Galois group $\Gamma$, where $X$ and $Y$ are smooth complex projective curve of genus $\geqslant 2$. In this paper, we study the moduli spaces of semistable $\Gamma-$invariant vector bundles on…

We propose new $G_2$-holonomy manifolds, which geometrize the Gaiotto-Kim 4d N=1 duality domain walls of 5d N=1 theories. These domain walls interpolate between different extended Coulomb branch phases of a given 5d superconformal field…

Let $F/{\mathbb Q}_p$ be a finite unramified extension, let $k$ be a finite extension of the residue field of $F$. We provide explicit constructions of integral structures for all rank two \'{e}tale Lubin-Tate $(\varphi,{\mathcal…

In this paper for each $n\ge g\ge 0$ we consider the moduli stack $\widetilde{\mathcal U}^{ns}_{g,n}$ of curves $(C,p_1,\ldots,p_n,v_1,\ldots,v_n)$ of arithmetic genus $g$ with $n$ smooth marked points $p_i$ and nonzero tangent vectors…

We study the moduli space M(G,A) of flat G-bundles on an Abelian surface A, where G is a compact, simple, simply connected, connected Lie group. Equivalently, M(G,A) is the (coarse) moduli space of s-equivalence classes of holomorphic…

We study the symplectomorphism groups $G_{\lambda}=Symp_0(M,\omega_{\lambda})$ of an arbitrary closed manifold M equipped with a 1-parameter family of symplectic forms $\omega_{\lambda}$ with variable cohomology class. We show that the…

We study special Lagrangian fibrations of $\mathrm{SU}(3)$-manifolds, not necessarily torsion-free. In the case where the fiber is a unimodular Lie group $G$, we decompose such $\mathrm{SU}(3)$-structures into triples of solder 1-forms,…

Let $C$ be a hyperelliptic curve of genus $g \geq 3$. We give a new description of the theta map for moduli spaces of rank 2 semistable vector bundles with trivial determinant. In orther to do this, we describe a fibration of (a birational…

Let $X$ be a compact Riemann surface, $\Gamma$ a finite group of automorphisms of $X$ and $G$ a connected reductive complex Lie group with center $Z$. If we equip this data with a homomorphism $\theta:\Gamma\to\text{Aut}(G)$ and a 2-cocycle…

In this note, we propose an extension of the relation between worldsheet global symmetries and structures over moduli spaces of superconformal field theories (SCFTs) to include noninvertible symmetries. The most familiar examples of such…

We give a purely algebraic construction of a cohomological field theory associated with a quasihomogeneous isolated hypersurface singularity W and a subgroup G of the diagonal group of symmetries of W. This theory can be viewed as an…

In this paper, we investigate the moduli of surfaces of general type admitting genus 2 fibrations with irregularity q = g_b + 1, where g_b >= 2 is the genus of the base. We prove that smooth fibrations are parametrized by a unique component…

Ricci flat manifolds of special holonomy are a rich framework as models of the extra dimensions in string/$M$-theory. At special points in vacuum moduli space, special kinds of singularities occur and demand a physical interpretation. In…

In recent work by Arena, Canning, Clader, Haburcak, Li, Mok, and Tamborini it was proven that for infinitely many values of $g$ and $n$, there exist non-tautological algebraic cohomology classes on the moduli space $\mathcal{M}_{g,n}$ of…

For a digraph $G$ without multisquares and a field $\mathbb{F}$, we construct a basis of the vector space of path $n$-chains $\Omega_n(G;\mathbb{F})$ for $n\geq 0$, generalising the basis of $\Omega_3(G;\mathbb{F})$ constructed by…